Please wait a minute...
浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (3): 315-321    DOI: 10.3785/j.issn.1008-9497.2020.03.008
数学与计算机科学     
左删失恒定应力部分加速寿命试验下逆Rayleigh分布的参数估计
龙兵1, 张忠占2
1.荆楚理工学院 数理学院，湖北荆门 448000
2.北京工业大学 应用数理学院，北京 100124
Parameter estimation of inverse Rayleigh distribution for constant-stress partially accelerated life tests with left censoring
LONG Bing1, ZHANG Zhongzhan2
1.School of Sciences, Jingchu University of Technology, Jingmen 448000, Hubei Province, China
2.College of Applied Sciences, Beijing University of Technology, Beijing 100124, China）;Parameter estimation of inverse Rayleigh distribution for constant-stress partially accelerated life tests with left censoring
 全文: PDF(433 KB)   HTML  
摘要： 在恒定应力部分加速寿命试验下，基于左删失样本,研究了逆Rayleigh分布的参数估计问题。运用极大似然法得到未知参数和加速因子的极大似然估计。根据Louis提出的缺失信息原则,计算了Fisher信息矩阵，得到分布参数和加速因子的近似置信区间。当取参数的先验分布为指数分布时，在平方损失函数下求得了参数的贝叶斯估计，并利用极大似然法估计了超参数。通过 Monte Carlo 模拟，得到估计量的均方误差，据此对极大似然估计和贝叶斯估计进行了比较。最后，计算了不同左删失样本下逆Rayleigh分布参数及加速因子的估计。
关键词： 逆Rayleigh分布;  左删失样本;  极大似然估计;  部分加速寿命试验;  加速因子    
Abstract: In the constant-stress partial accelerated life test, estimation of the parameter for inverse Rayleigh distribution is studied based on left censored samples. Maximum likelihood method is used to obtain the maximum likelihood estimations of the unknown parameter and acceleration factor. The Fisher information matrix is calculated according to the principle of missing information proposed by Louis, meanwhile the approximate confidence intervals of the distributed parameter and the acceleration factor are obtained. When the prior distributions of the parameters are exponential distribution, the Bayesian estimations of the parameters are obtained under the square loss function, and the maximum likelihood method is used to get the estimations of the super parameters. The mean square errors of the estimators are calculated by Monte Carlo simulation, based on these, the maximum likelihood estimation and Bayesian estimation are compared. Finally, the parameter of the inverse Rayleigh distribution and the estimation of acceleration factor are calculated for different left censored samples.
Key words: maximum likelihood estimation    inverse Rayleigh distribution    partially accelerated life tests    left censored samples    acceleration factor
收稿日期: 2018-06-12 出版日期: 2020-06-25
CLC:  O 213  
基金资助: 国家自然科学基金资助项目（11771032）；湖北省教育厅科研项目（B2016261).
作者简介: 龙兵（1973—），ORCID:http://orcid.org/0000-0003-3638-3026, 男，硕士，教授，主要从事可靠性理论及应用研究，E-mail:qh-longbing@163.com.
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章　　
龙兵
张忠占

引用本文:

龙兵, 张忠占. 左删失恒定应力部分加速寿命试验下逆Rayleigh分布的参数估计[J]. 浙江大学学报（理学版）, 2020, 47(3): 315-321.

LONG Bing, ZHANG Zhongzhan. Parameter estimation of inverse Rayleigh distribution for constant-stress partially accelerated life tests with left censoring. Journal of Zhejiang University (Science Edition), 2020, 47(3): 315-321.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.03.008    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I3/315

1 ISMAIL A A. On designing constant-stress partially accelerated life tests under time-censoring[J]. Strength of Materials, 2014, 46(1): 132-139.
2 SMAIL A A. Reliability analysis under constant-stress partially accelerated life tests using hybrid censored data from Weibull distribution[J]. Hacettepe Journal of Mathematics and Statistics, 2016, 45(1):181-193. DOI:10.15672/hjms.20157211089
3 ISMAIL A A, AL-BABTAIN A A. Planning failure-censored constant-stress partially accelerated life test[J]. Systems Engineering and Electronics, 2015, 26 (3): 644-650.
4 ISMAIL A A, TAMIM A I A. Optimum constant-stress partially accelerated life test plans using type-I censored data from the inverse Weibull distribution[J]. Strength of Materials, 2017, 49(6):847-855.DOI:10.1007/s11223-018-9930-8
5 ISMAIL A A. Bayesian estimation under constant-stress partially accelerated life test for Pareto distribution with type-I censoring[J]. Strength of Materials, 2015, 47(4):633-641.DOI:10.1007/s11223-015-9699-y
6 HASSAN A S, ASSAR S M, ZAKY A N. Constant-stress partially accelerated life tests for inverted Weibull distribution with multiple censored data[J]. International Journal of Advanced Statistics and Probability, 2015, 3(1):72-82.DOI:10.14419/ijasp.v3i1.4418
7 JEBELY F， ZARE M K, DEIR E. Efficient estimation of the PDF and the CDF of the inverse Rayleigh distribution[J]. Journal of Statistical Computation and Simulation, 2018,88(1):75-88.DOI:10.1080/00949655.2017.1378656
8 ALI S. Mixture of the inverse Rayleigh distribution: Properties and estimation in a Bayesian framework[J]. Applied Mathematical Modelling, 2015, 39(2):515-530.
9 SOLIMAN A, ESSAM A A, ALAA A A. Estimation and prediction from inverse Rayleigh distribution based on lower record values[J]. Applied Mathematical Sciences, 2010,4(62): 3057-3066.
10 SANKU D,TANUJIT D. Bayesian estimation and prediction on inverse Rayleigh distribution[J]. International Journal of Information and Management Sciences, 2011,22: 343-356.
11 NAVID F, MUHAMMAD A. On posterior analysis of inverse Rayleigh distribution under singly and doubly type II censored data[J]. International Journal of Probability and Statistics, 2012, 1(5): 145-152.
12 LOUIS T A. Finding the observed information matrix when using the EM algorithm[J]. Journal of the Royal Statistica Society, Series B(Methodological), 1982, 44(2): 226-233.
13 程从华. 生存分析中删失数据统计推断及其应用[D].兰州：兰州大学, 2011. CHENG C H. Statistical Inference and Its Application of Censored Data in Survival Analysis[D]. Lanzhou: Lanzhou University, 2011.
[1] 徐明民,晏晓林. 三参数威布尔分布有替换定时截尾试验的极大似然估计[J]. 浙江大学学报（理学版）, 1998, 25(2): 24-29.